Question: Determine where $f(x)$ intersects the $x$ -axis. $f(x) = (x - 9)^2 - 49$
Solution: The function intersects the $x$ -axis where $f(x) = 0$ , so solve the equation: $ (x - 9)^2 - 49 = 0$ Add $49$ to both sides so we can start isolating $x$ on the left: $ (x - 9)^2 = 49$ Take the square root of both sides to get rid of the exponent. $ \sqrt{(x - 9)^2} = \pm \sqrt{49}$ Be sure to consider both positive and negative $7$ , since squaring either one results in $49$ $ x - 9 = \pm 7$ Add $9$ to both sides to isolate $x$ on the left: $ x = 9 \pm 7$ Add and subtract $7$ to find the two possible solutions: $ x = 16 \text{or} x = 2$